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The days when cellphone users could get all the Internet, video, and downloads they want for a flat monthly fee are fading, as Verizon Wireless becomes the latest cellphone carrier to do away with unlimited data plans.

Beginning tomorrow, Verizon Wireless, the nation’s second-largest wireless carrier, will cap the amount of data downloads allowed under its $30-a-month wireless broadband plan; it will also unveil more costly options for users with big appetites for digital data.

The changes will affect only new customers. Customers who now have unlimited data plans, or who sign with Verizon today, will be able to continue paying a flat fee for all the data they wish to download.

Verizon follows the country’s number one carrier, AT&T Inc., which did away with unlimited data plans last year. The smallest of the nation’s top four cellular companies, T-Mobile USA, still offers an unlimited service, but the company dramatically slows down data transfers for heavy users - in effect, imposing a speed limit instead of a usage quota. Of the top wireless companies, only Sprint Nextel Corp. still offers unlimited data plans.

The trend follows an explosion in the amount of digital information sent and received as more people buy devices like Apple Inc.’s iPhone and smartphones running Google Inc.’s Android operating system. With limited network capacity, cellphone carriers can discourage heavy usage by placing caps on data transfers and charging more. “What we’re trying to do is streamline our data plan,’’ said a Verizon Wireless spokesman, Howard Waterman.

Limited plans “will certainly affect consumer behavior,’’ said Craig Moffett, a cellular industry analyst for Sanford C. Bernstein Co. in New York. “If it’s going to cost more for the consumer to watch a video, they’re going to think twice before they click on that link of the squirrel on water skis.’’

Verizon Wireless subscribers now pay $29.99 a month for as much data as they want. That means unlimited access to e-mails, Web pages, and entertainment services that stream music, video clips, or movies.

After tomorrow, Verizon Wireless will allow new customers to send and receive a limit of 2 gigabytes of data per month for $30 - enough, said Waterman, to send 1,000 e-mails, view 100 Web pages, listen to more than 20 hours of streaming music, upload more than 20 photographs, and view over two hours of high-definition video.

Verizon will offer higher-priced plans for consumers who use more data. Consumers will be able to buy 5 gigabytes of data per month for $50, or 10 gigabytes for $80. Users who exceed their quotas will be billed $10 per extra gigabyte.

Edgar Dworsky, a former Massachusetts assistant attorney general who now runs the consumer education website consumerworld.org, noted that Verizon’s new plan lacks a low-priced option for consumers who use very little wireless data. AT&T, for instance, charges $15 a month for 200 megabytes of data, but at Verizon, the lowest-priced plan will be $30 a month, the price it now charges for unlimited data.

“What used to be the cap has become the floor,’’ said Dworsky. “They probably see it as a good moneymaking opportunity.’’

Waterman said that 95 percent of Verizon Wireless customers use less than the 2 gigabytes per month limit. However, Parul Desai, telecommunication policy counsel for Consumers Union, the nonprofit group that publishes Consumer Reports magazine, said even users who do not exceed the cap might cut back on usage anyway, to avoid accidentally going over the limit. “Maybe you won’t use Netflix,’’ Desai said, “or maybe you won’t try some new application.’’

Verizon Wireless plans to reassure worried customers by notifying them about how much they have used of their monthly data quota. A new service will send a free text message to smartphone users when they have used half their quota, with additional messages when the level reaches 75, 90, or 100 percent. Verizon Wireless will also warn users who have already crossed the line, texting them when usage hits 110 percent.

Meanwhile, Sprint said it sees no need to change its unlimited cellular data plan. The carrier offers 450 minutes of talk, unlimited calls to other cellphones, and unlimited data on Sprint’s 3G or 4G networks for $79.99 a month.

Even as they build faster networks, cellular companies will discourage consumers from downloading more data because the companies have only so much bandwidth to carry the traffic, said Neil Strother, mobile services analyst at ABI Research Inc. in Oyster Bay, N.Y. “Wireless networks do have potential capacity constraints,’’ he said.

Landline cable or telephone companies can increase capacity by adding more cables, he added, but wireless companies must move voice and data over a limited spectrum of radio frequencies.

Amy Storey, a spokeswoman for CTIA, the cellular industry’s chief trade association, said the move toward wireless data caps underscores the need for federal regulators to provide more radio frequencies for use by cellphone companies. “Right now, the amount of spectrum we have available is not enough to meet consumer demand,’’ she said.

There is considerable evidence of a radio spectrum shortage. AT&T has said that its $39 billion bid to acquire rival T-Mobile USA is chiefly an effort to get access to T-Mobile’s radio frequencies. The deal would allow AT&T to quickly upgrade its cellular services.

Meanwhile, the cellular industry and the Federal Communications Commission are pressuring television broadcasters to sell some of the unused frequencies they currently control to wireless phone carriers.